page_title: Robert Emden
section_title: Influence in physics and meteorology
hierarchical_section_title: Robert Emden / Influence in physics and meteorology
caption_attribution_description: English: Oblique view of Emden, on the far side of the moon, facing west.
context_page_description: Jacob Robert Emden was a Swiss astrophysicist and meteorologist. He is best known for his book, Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische probleme, published in 1907. It presents a mathematical model of the behaviour of polytropic gaseous stellar objects under the influence their own gravity, known as the Lane-Emden equation.
context_section_description: Most of Emden's work related to thermodynamics applied to natural phenomena, while his published papers focused on geophysics and astrophysics.
  Emden's book Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische probleme presented a mathematical model to explain the expansion and compression of gas spheres. The book also includes a short section on Karl Schwarzschild's theory of convective equilibrium. 
  Emden's work, in conjunction with  Subrahmanyan Chandrasekhar, was named the Emden–Chandrasekhar equation.  In a major advance over previous work, by introducing polytropic solutions, modelling of a much broader range of stellar objects was possible.
  His theories also suggested that stars have a boundary at a finite radius. This work, in conjunction with Jonathan Homer Lane, became known as the Lane-Emden equation. The Lane-Emden equation can be described as "a second-order ordinary differential equation that applies to polytropic profiles in density". The Lane-Emden equations were later studied by Ralph H. Fowler who developed a new set of solutions for different values of n and for all types of boundary conditions. These became known as Emden-Fowler-type differential equations. Emden's convective stellar models have been supplanted by radiative theory.
  Robert Emden also offered an hypothesis, which has since been discredited, to explain sunspots.
  The crater Emden on the Moon is named after him.
caption: Emden Crater
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